This post sprang from two things:
charlottehywd's post
"A Thought on Hogwarts Schooling", and
this comment over on an old Snapedom essay. One line of the comment says, "You can't very well collect gold from unsuspecting Muggle households (or the Muggle government) while still keeping the whole existence of the WW a secret."
But... maybe they can.
What's to stop Hogwarts (other than wizarding foolishness) from owning a nice portfolio of Georgian townhomes, warehouses, and personal storage facilities as an absentee landlord? All they need to do is establish a Muggle business as a front, employ a few Squibs to manage the bookkeeping and hiring of Muggle property managers and such, sit back, and enjoy that steady income stream. They've had a thousand years to acquire property, so they could own quite a lot by now.
The Ministry and St. Mungo's could have their own Muggle real estate holdings. The Ministry might be in an especially good position if they have a claim to the property of any witches or wizards who die without heirs. We know that many magical homes are in Muggle neighborhoods; send in a cleaning squad to remove any magical modifications and creatures, and voila! Another home to rent to Muggles! Country homes with enough land could be razed and sold to developers for some quick cash.
(And a savvy but unscrupulous entrepreneur might realize that once embezzled Muggle money enters the wizarding world, it's untraceable. If you are, say, a Squib accountant, you could probably make a nice living skimming funds from Muggle companies. A magical business partner and/or the Ministry could very easily frame a Muggle employee for embezzling the money when necessary. The framed parties might even believe they're guilty! No wonder the Weasleys don't like to talk about that cousin.)
Maybe wizards don't pay for any of their major social institutions. As far as they're concerned, services just appear like, well, magic.
Of course, all this Muggle money has to be changed into Galleons somehow, and that means it all goes through the Gringotts goblins. I bet that isn't a friction-free process....
What other ways could the wizarding world leech off the non-magical one for its funding?